Proportionally editing an object using a given/exact angle
First, make yourself aware of the trigonometrical relations.
$height =  tan(\alpha) = tan(63°)$
In python you can express this as
tan(radians(63))

This is the desired height. Add a cylinder, select the top edge loop and type the equation into the Z field. Upon pressing enter, the value will automatically be calculated.

Scale the top edge loop to 0, add a half sphere, add appropriate loop cuts if necessary, then merge the top circle into a single vertex.